{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Component Analysis - Key Ideas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA finds principal components as linear combinations of the existing features and uses these components to represent the original data. The number of components is a hyperparameter that determines the target dimensionality and needs to be equal to or smaller than the number of observations or columns, whichever is smaller. \n",
    "\n",
    "PCA aims to capture most of the variance in the data, to make it easy to recover the original features, and that each component adds information. It reduces dimensionality by projecting the original data into the principal component space. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:11.982134Z",
     "start_time": "2018-12-27T18:10:11.775104Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy.linalg import lstsq\n",
    "from numpy.random import randn, seed\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Patch\n",
    "import seaborn as sns\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:13.243169Z",
     "start_time": "2018-12-27T18:10:13.241003Z"
    }
   },
   "outputs": [],
   "source": [
    "# plt.style.use('fivethirtyeight')\n",
    "sns.set_style('whitegrid')\n",
    "pd.options.display.float_format = '{:,.2f}'.format\n",
    "seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear Projection: Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PCA algorithm works by identifying a sequence of principal components, each of which aligns with the direction of maximum variance in the data after accounting for variation captured by previously computed components. The sequential optimization also ensures that new components are not correlated with existing components so that the resulting set constitutes an orthogonal basis for a vector space.\n",
    "\n",
    "This new basis corresponds to a rotated version of the original basis so that the new axes point in the direction of successively decreasing variance. The decline in the amount of variance of the original data explained by each principal component reflects the extent of correlation among the original features. The number of components that captures, e.g., 95% of the original variation relative to the total number of features provides insights into the linearly independent information in the original data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figures illustrates several aspects of PCA for a two-dimensional random data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Create Noisy, Correlated Data from Signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.458364Z",
     "start_time": "2018-12-27T18:10:20.107454Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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lmMpGB/bUfo3xHofqwRLLEFaJcwnjhUFIlED8h5v7zp6IergZaUGzEgue9b6bxB+DkCiBKDHcjDR3F+zvvb8dzcOYAq/X264SgMtniBKKEmvwIi2jCfz7NZ+cUuyh61o9wD0SBiFRAvEONx8Z2i/qYXGkMA18tnDDl98othNEj7tKAA6NiRJOcX4GMk1XYLOpM3cX+GzhLgDmJBPcXbE/PEmvBRQGIZGAIlWDA58tPK0oF1ednb7gWrQ7uoet67WAwiAkShD+RYZMk7q/FSywKhsd2FJ7HtVnLqPD3RX1Imm97SoBNA7CkydP4vXXX8fmzZtx/vx5LFiwACaTCXl5eVi8eDGSkjiFSQTcXMl9sehWqPhQNwA3nx/o/X0vvS+SlkOzpNm4cSMWLlwIl8sFAFi+fDlmz56NLVu2wOPx4JNPPtGqaUS6E1hk+PSrds1+30tPc3yx0iwIs7OzsXbtWt/rhoYG3HPPPQCAMWPG4MiRI1o1jUh3Aiu9Iwb1Dnu9kucOBv5+ijkJY4em63rvsFyaDY3HjRuHixcv+l57PB6YTN0TH6mpqbh69WrE73C5XLDb7ZJ+z+l0Sr7WCHi/xpJpAl4suhWfftWOEYN6o2CgOeT9Hm1uw4pDl+Bye7DtWDMWjBmIUdmpiv5+9/ddgd1+JabvlUrtf766KZb4zwe2tbWhX79+ET9jsVhgkzhRYrfbJV9rBLxf47HZgKnf/jnc/W49VQ+X2wMAcLk9OOe0YqoC/9v4/74cSuwkifafr9Tw1E01Ij8/H7W1tQCAQ4cOYeTIkRq3iCgxyd19ovQwOvC79biTJJBugnD+/PlYu3YtHn/8cXR2dmLcuHFaN4koIck5AVrtoNLrTpJAmg6NMzMzsX37dgBAbm4u3n33XS2bQ6S6eB04IHWtntpnBup1J0kg3cwREhmdHk9sVjuo9LqTJBCDkChO9Hhic7igUqr3qsedJIEYhERxEq9hotwAC3VmoN56r2piEBLFSTyGiUoFmB57r2piEBLFkdrDxFgCzL8nmShFDqUwCIniLNTQVYk5uXABFu77g/UkE6HIoRQGIVEchRq6KjWkDTX8jvT9wXqSSycMN3wAeulmQTWRCEItMFZy4XFxfsZNIRbp+6N9Foqau1LiiUFIFEehAkeJhzJF87tecnajeCXK9jkpODQmiqNQQ1e1K8pSvl9uIcdIlWUGIVGchQqccEGkRIFF6Yq1kSrLDEIinQkMt2CFjkyT9oueE2X7nBQMQiIdCRZuwYagk4eY4zI0jdTjTITtc1KwWEKkI8HCTckCi5wqr5GKIZEwCIniQGoABQu3UBVduZVeucGWKGcJKoFDYyKVyZnLC1dVjnVoKncobaRiSCQMQiKVyQ2gaOfdIs3nyQ02IxVDImEQEqksHj0rKb1O/2Dra032DXW9lelggWeUYkgkDEIilUXTs5J7AMOW2vOSep3e9/xDc1pRLt6qOifM2YPBMAiJ4kDOYmm56wMrGx2oPnPZ9zrFnOTrdQYL1MCh+r7Gvxtmh0i0WDUm0lCwSq7cau3h0y3ocHf5Xt83+JYegRpYJQ6sTD+Q/79V3eecCNgjJNJQqHWDcuYUA6+fUpgT8ru9PdPAoXpBVn8hiiKhMAiJ4iTYMDVY6EWaU6xsdGBP7dcY73GEDLZQ3+0VOFQXpSgSCoOQKA5CzfvJXTfo/z37zp7o8T3hqsSBh7SK3PsLhkFIFAfh1hLGsih6S+15WWsStT6oQa9YLCGKg0j7guVswUsx3/jPtvrMZVl7gEXaNicHg5AoDsLtC5azB7g4PwP3Db7F97rD3SUrzNQ+CTtRcWhMFCehhsByt+BNKczBkTNfw+X2yA4zkbbNycEgJFKBnIJENHuAF4wZiHNOa1RhJnqFOBgGIZHC5BYkoumljcpOxVSbTclmC41BSKSwaE6OVquXxqUy0rBYQqQwvRQkRDphOlbsERIpTC8FCTWeaWLUHiaDkEgFeihIjM5Lx/vHLqDD3dXjRJpoGXkxNofGRCSJkRdjMwiJDMr/eC65C6+D0cvcpxo4NCYyKKUfEaCXuU81MAiJDEqN4NLD3KcaGIREOhZrldaowaU0zhES6RTXAcYPg5BIp4xcpdUbBiGRThm5Sqs3nCMk8qOnnRNGrtLqDYOQ6Ft63DkRTbFDT2GeKDg0JvqWEebkWGCJDoOQ6FvxmpOT+nySaBghzLXAoTHRt2Kdkws1JPV/H4Cqw2+ld5OIgkFI5CfYnJyUObdQ84uB74+6bYDiR2MFtp8FFvkYhERhSC2ghDr7L/D9U46rSDEnocPdpVqPjbtJ5OMcIVEYUufc/OcXzUkm9LUm3/Q+AHz5f50AgLFD03VRlaZuDEISjpRihfeavtZkSQWU4vwMTCvKhdkEuLs8eKvqHCobHb6h6tCMNN+1He4uZA3oAwCqFU1IHg6NSShShrr+1/RONmNaUS6uOjsjzrlddXbC7en+s//w2PsZ/+/sa03W3ZpFkekuCB999FH07dsXAJCZmYnly5dr3CIyEinP8Qi85qqzE0snDI/43eEqtoFFDDWeJ0LR01UQulwuAMDmzZs1bgkZlZTlJdEuQYlUsQ0sYnCZi37oKgg///xztLe3Y9q0abh+/TrmzJmDgoICrZtFBiJleUksS1CkVmy5zEVfTB6Px6N1I7yamppw8uRJlJSU4IsvvsAzzzyDjz76CL16Bc/ruro6WCwWSd/tdDphtVqVbK6uiXy/R5vb8OlX7RgxqDdGZaeq8nvx+I1wRP7nK5fNZot4ja56hLm5ucjJyYHJZEJubi769++PlpYWfPe73w16vcVikXSTAGC32yVfawSi3m9lowOvVZ1He6cb+862Yc3kLMUPLVDiN2L19t7jOOd0C9ObjPbfZ7vdLuk6XS2f+eCDD7BixQoAgMPhQGtrK9LTOXdC0sW611bKoQVa7+etbHRgxaFLPFhBQboKwokTJ+Lq1auYPHkyXnjhBVRUVIQcFhMFE+vBCVJCTusDUw+fboHr23U6PFhBGbpKmZSUFKxatUrrZlACi7UIIaVirHWhY3ReOrYda4bL7WHFWSG6CkIiJcSy11ZqyMVrP2+w+cri/AwsGDMQ55xWYeYI1cYgJEM42tyGrafqFQkGvRxaEG4XzKjsVEwVqBimNl3NERJFwyjFg8A90FoXZUTCIKSEZ4TiQbBqdbiizNHmNh7YoCAGISW80XnpsJhNAOJfxVXq2P1Qe4/XTL4bT92b02NYHKoHrOYjAIyOc4SU8LQqHij51LtQ1epg85WhesA8zSZ67BGSIYzKTsXSCcPj+h+/knN4oXp/wQTrAXM+MTbsERJFSekHJck5sCFYD5in2USPQUgUJW8vbkvt+bj/duDyGa0XeSc6BiEJS8rT6aQ4evYK2jvdOHr2iqZzc3pZ/5iIGIQkpFgKHf4BypOmjYHFEhJStMWFwPV+Uh/uFAsui1Efe4QkpGgLHcGeZxJpbi6WIbiSS3QoNAYhCSna4kKwAA03NxdrkHHoHR8MQhKW3OKCt2cn9fGeQOxBpvQSHQqOQUj0rXBD2MBnHUvt2cUaZFwWEx8MQiJEHsJG27NTIsi4LEZ9rBoTIXIVOZbj+YvzM+K+/Y/kYY+QCJGHsByiGhuDkBJeZaMDe2q/xniPQ9Uj+jlENS4GISU0/7m9fWdPxLTOTk7QKbU9j/SBc4SU0OJx/FTgzg4pzz6mxMIgpISm9jOGg4VevM7+49a6+GEQUkLzzu09MrSfKtvPgoVePB7wzl5nfHGOkBJecX4GMk1XYLMpP1cXakud2hVkbq2LLwYhURihQk/tCjK31sUXg5AogmhCL9aqMtctxheDkEhhSh2dxXWL8cNiCZFEUqu4fKJc4mEQklCiXZIip4obj6oyKYtDYxJGLEPWSFXcwDlBzu8lFgYhCSMwzLbUno/pZGqvUAHLAEwcHBqTIRxtbos45B2dl44U841/5avPXJY8RPb28p66N0fSWYWUWBiElPAqGx1YcehSxPm74vwM3Df4Ft/rDndXyNAKNpcY6lzBUHOC3CKXOBiElPAOn26By+0BELlHNqUwJ2IhQ+72tmC9RW6RSyycI6SE5F+cGJ2Xjm3HmuFyeyJWaaUUMqLZ3hY4J8gtcomFQUi6ImVHRrDixIIxA3HOaZVUpY1UyFBiexu3yCUWBiHphtTlLcF6W5OHpGKqzaZIO5R64BKX0CQOBiHphtThZPDe1hVF26LE8hcuoUkcLJaQbkjdkRFuKQtRNNgjJN2QM5xkb4uUxCAkXWHAkRY4NCYi4TEIiUh4DEIiEh6DkIiEx2IJGUaszwkhcTEIyRCONrfhtarzMT8nhMTEoTElnGDHW336VbusMwF5RBb5YxBSQgl1vNWIQb0lPyeER2RRIAYhJZRQp0GPyk6VvO2OJ0pTIAYhJZRw+5FDnSAt5ztITLoqlnR1dWHJkiVoampCSkoKysvLkZOTo3WzSAHRVHSDfSba463CPWUOABbtrme1WWC6CsJ9+/aho6MD27ZtQ11dHVasWIH169dr3SyKUTSP0Qz3Gbn7kcM9ZS6WR3yScehqaPyXv/wFo0ePBgAUFBSgvr5e4xaREqKZk1NyHi/cd0n9HVaZjU1XPcLW1lakpaX5XpvNZly/fh29egVvpsvlgt1ul/TdTqdT8rVGoKf7zbU6YTGb4HJ7YDGbkGuN3Db/zyQnAfbmS3h773GMyk4Nen24+w33+1LadrS5DSsOXYLL7cG2Y81YMGZgyHbEi57++caD2verqyBMS0tDW1ub73VXV1fIEAQAi8UCm8Tj2e12u+RrjUBP92uzAZlZ8uYIvZ/ZUnse1Wcu4/982Y76Sx1YMzkr6OfD3W+435fStq2n6n1PyXO5PTjntCr2WIBo6emfbzxEe79Sw1NXQThixAjs378fDz/8MOrq6jBkyBCtm0QKieacweL8DBw+3YIOd/dw1f/4frnFl3C/H4+HOZG+6SoIi4uLUV1djUmTJsHj8aCiokLrJpHGgoXQyr1N2HDwr3B3eXwFjkxT8M8rsf+YD2IyPl0FYVJSEpYuXap1M0hHgi112XDgDL4dqfo9xc5802f9K8LvH7uA+wbfgimFOVE/lY4BaFySq8bV1dVYuHChb8y9bds21RpFFMrh0y2+EAQAc5Ip5FDVvyLc4e7C/qYWbqmjoCQH4ZYtW/Diiy9iz549qKmpEapiRdoJ3Bfc15rs2xViNgEzfnx7yJ6a/w4SL26po2AkB+GAAQPQr18/zJ8/H9XV1fjss8/UbBcRgJvX+V11dvr2FG8oHYmycUNDftY7rB47NB0p5u5/1QOLHVwfSICMOcIf//jHvj/PmzcPmzdvVqVBRP6CFUvkzNf57yAJLHZwVwl5RewRLlu2DB6PBw888ECP90tLS1VrFJGXUg9zD3YgA0+hIa+IQdinTx88++yzaG9vBwBUVVVh0qRJqjeMjCfUMFSr4WmoU2g4XBZPxKHxCy+8gA8//BBPPvkkUlJS0KdPH8ybNy8ebSMDCTUMjTQ8VXP4Gmx9IIfLYorYI6ypqcH27dvRp08fXLlyBf/xH/+BkSNHxqNtZCChhqGRhqfRDF9X7m3CuNUHsXJvU8RrA4fMHC6LKWIQrl+/Hs8//zw2b96MNWvW4IUXXkBNTU082kYGEmoY6v++OcmEvtZkSZ8LZeXeJvxu/xk0OVrxu/1nJIVhLL9HxhBxaPzOO+/4/jx06FBs3LgRs2bNwr333qtqw8hYQm1TK87PwLSi3O7dIl0evFV1DgVZ/aM+iPWPn1686XW4JTZS20nGJnuL3cCBA/GHP/xBhaaQ0YVa9nLV2XnTljn/6+Qsl/lfaRZ8+f+cPV4r1U4yrqgOZrVarUq3gwSm5HD0+Z/moVdS9wkMvZJMeP6neYq0kYxNV4cukJiUHI4W52dg/ZM/4NCWZGEQki4EDkdjOT6LQ1uSi0FIAJQ5t0/JtnAtH8WTrh7eRNoIPOFF6x0VXMtH8cYgJN0FT2DxpK81mVveSFUcGpMunskR6gHsfa3JeKvqHIfJpCoGIWm+iDjcA9gX7a4PuTVPD/OZZAwcGhOA4MdUxUu4oXmwYbKe5jPJGBiEpLlwC6oDzyO86uzU1XwmGQOHxqSSKHMWAAAZZ0lEQVS5SEPzwHWBWs9nkvEwCEkXpC6C1no+k4yJQUiqCrVQmztHSE84R0iqCbVQW28LuIkYhKQaqadSb6k9zwXTpCkGIalGyqnUKeYkVJ+5zN4haYpzhKSacKdSe9+/cOUa9jd19xSDHcpKFA8MQlJVqMKG/4PXj569wuUwpCkGIUWk5BFdgd/F5TCkBwxCCkvJswHD7SlmAJKWWCyhsJQ8oktvx30ReTEIKSwlH6zEZwaTXnFoTGHJmcOLNJfI+UDSKwYhRSRlDm/l3iZsOPhXuLs8YecSOR9IesShMflUNjqi2uGxcm8Tfrf/DNxd3U9pD5z/k/K90f52OGp8JxkTg5AARL//t7LRgQ0H/9rjPXOSyTf/J+V71dh7zP3MJAeDkADIr+h6e1tbas/7eoJeM358u2/4K+V71agms0JNcjAICYC8iq5/b6v6zGWkmLv/NTInmfDc2MEoGzdU1veqUU1mhZrkYLGEAMir6Pr3tjrcXRg7NB1ZA/qEPF060veqUU1mhZrkYBCSj9SKbuDjP6cU5oT9nJTvVaOazAo1ScUgJNnY2yKjYRBSVNjbIiNhEJKPkqfMECUSBiEBUPaUGTm/yeAlPeDyGQJw87q71/d+ruoiZC54Jj1hEBKAnuvuAKDJ0apqQHHBM+kJg5AAdBc/phXlon/vG7MlagYUFzyTnnCO0OCkzsNVNjrwVtU5Xy8NUCagQv0+l+CQnjAIDUxOAcR/qAoAQzPSMG/cHbIDyj/4AIT9fS7BIb3g0NjA5MzDBQ5VA0NQ6lFa/gWQLbXnOQ9ICYE9QgML3AoXbpgbbqgqtWcZGHxAd6jyUZ2kd7oJQo/HgzFjxuD73/8+AKCgoABz587VtlEJTu48XKiharCeZeB1lY0OVJ+57HudYk7ClMIcTCnM4Twg6Z5ugrC5uRnDhg3Dhg0btG6KoUSah5NSTJHSszx8ugUd7i7f6/sG3+L7PgYg6Z1u5ggbGhrgcDhQWlqKZ555BmfPntW6SYYndVGzt2c5dmg6Rt02wPdZ/znDwDnGKYU58bkJIgWYPB6PJ/JlytqxYwc2bdrU471Fixbh8uXLeOihh3D8+HEsX74cO3fuDPs9dXV1sFgskn7T6XTCarVG3eZEI+V+3zz6NT5s+sb3+pGh/fCrUbcGvfZocxtWHLoEl9uDXkmACUBnF2Axm7BgzECMyk7F0eY2fPpVO0YM6o1R2alK3k5E/OdrbLHcr81mi3iNJkPjkpISlJSU9Hivvb0dZnN3j2LkyJFwOBzweDwwmUwhv8disUi6SQCw2+2SrzUCKfc73uPAvrMnfEPe8YVDYLMFH8ZuPVUPl7v7/zOv3xgBw+X24JzTiqk2G2w2YKpidyAP//kaW7T3a7fbJV2nm6HxunXrfL3Ezz//HIMGDQobghQ775D3qXtzIh6y4D/0TTEn+Y7nTzEn4cKVa9wrTAlNN8WS6dOno6ysDAcPHoTZbMby5cu1bpIQQhVTAosogRVooHu5TPWZy9jf1IKjZ6/E5cQaIjXoJgi/853v4L/+67+0bkbC8wZYrtWJaEdOodYNBoZmd6W4e5F0qGU1RIlAN0Njip1/FXjFoUtRD1el7kjhwQlkFAxCA/EPMJfb4wswKdvj/EkNODlzjER6ppuhMcXOf+GzxWzC6Lz0qE6e5skwJBoGYYIKtiPEP8ByrU4U52dg0e76iNvjgpFyMowWx/sTqYFD4wQUbkdIcX4GRuel49Ov2lHZ6FB1Ho+nTJNRMAgTULgAWrm3CTPe/Qs+bPoGs7aeAADV5vFYLCGjYBAmoFABVNnowIYDZ+Du6t4B4j8UXjphOADIKppEEqlYIrdIQ6QVzhEmoFDFjMOnW+D22zluTjL1CEml5vOCLbYOdg3nDylRsEeYoLy9PP9w8e8pJgGY8ePbe4SkEvN5Uk+s4enUlEgYhAbiP1T9zdgMlI0b6vu7wL3C0e4PlhKowQ5p5fwh6RmD0GC8PcXAY7D8zxQEgP1NLZKfW+w/1yelQBLukFYiPWIQxpHWxYPi/AxkDejjCykpQ9bAoTAQuQrNQ1op0bBYEid6KR7IeaATEHwoHDg3GYg7UyjRMAjjRMoDkOJBbkjJDU7/32EAUqJgEMZJtIGiBjkhxd4diYBBGCdqB4qUp9FFi707MjoGYRypFSjB5h8zTTdfw14dUXCsGhtApLV9/pXfGZuPY+XeJsnfrXWlmygeGIQGEGltn39Quj3AhoN/lbx+UMouEqJExyA0gEiHH4zOS4fZb6js7vJI2vLGY7ZIFAzCBBRsuBps77H/3824fzDMSd1pKLVqzWO2SBQsliSQykaH7xGaHe4uWQuzy8YNRUFWf1kFEy6dIVEwCBOEf2XYKx4Ls7l0hkTAINQ577KXC1eu9QhBQN5wVS9b/Ij0iEGoY/7hlWJOQoo5CR3uLqSYk3Df4FswpTBHcpjpZYsfkR4xCHXMP7w63F0YOzQdWQP6RDVfp6ctfkR6wyDUIe9wuK81Gb2Tzb7wktMDDMTCB1FoDEKd8R8O9042Y1pRLq46OxUJLxY+iIJjEOpM4FzeVWen7wl0SuP+Y6JuXFCtMrl7deUuYo52LzC3zxHdwB6hiqJZsuI/l9fXmuzb1qb0IzNZRSa6gT1CFcndq+vt3QHdPcO3qs6F7bEF+37vdxxtbgv7W9w+R3QDe4QqkrNkJbB3N+q2ARF7bIHf/3VrB2ZsPg63B7CYTcjMcoTs5QWrInPOkETFIFSRnCUrgb07AD2WzoQK0VG3DQAA5A/6DjYc/Cvcnu73XW5PxOGufxWZO09IZAxClUldshLYu5tSmIMphTkhQzRwmQ3QfbyWV9K33ykV5wxJZAxCnQjVewwVRuF6kOYkE0qG9QsbZIHDYO48IZExCHUkWO8x1LxdpB5kpulKyN8JNQzmzhMSFYNQx8LN20XqQdrtoYMw1DCYO09IVFw+o2ORlt+EO5U6HC6dIeqJPUIdU2vejsNgop4YhDqmZmBxGEx0A4NQ5xhYROrjHCERCY89Qp3g9jYi7bBHqAM8EotIWwxCHZB7So2/aM8jJKIbGIQ6EO26PvYkiZTBOcIYKDWvF+0yGR6UQKQMBmGUlD62KpplMjwogUgZDMIoye2NVTY6sKX2PADE9FhOf9whQqQMBmGU5J4+/dx7n6LD3QUAqD5zGb97YoRiYcgAJIoNgzBKck+f9oYgAHS4uzifR6QjmlaNKysrMXfuXN/ruro6lJSUYNKkSVi3bp2GLbsh3PIUqae/jM5LR4r5xv/UKeYkzucR6YhmPcLy8nJUVVXBZrP53lu8eDHWrl2LrKwsTJ8+HQ0NDRg2bJhWTYxYEJFaNS7Oz8DvnhgR0xwhd54QqUezHuGIESOwZMkS3+vW1lZ0dHQgOzsbJpMJRUVFqKmp0ap5AMIvdJa7hq84PwNvT70Hb0+9BwBkLYLmekEidaneI9yxYwc2bdrU472Kigo8/PDDqK2t9b3X2tqKtLQ03+vU1FRcuHAh7He7XC7Y7XZJ7XA6nZKv9cq1OmExm+Bye2Axm5BrvfEde2q/7hGSe2pPhT0e3+tocxtWHLoEl9uDbceasWDMQIzKTg37mWh+K5r7TWS8X2NT+35VD8KSkhKUlJREvC4tLQ1tbTceSt7W1oZ+/fqF/YzFYukxtA7HbrdLvtbLZgMys4IPScd7HNh39sZT5MYXDoHNFnnIuvVUPVzfPnPT5fbgnNOKqRHaFc1vRXO/iYz3a2zR3q/U8NRN1TgtLQ3Jyclobm5GVlYWqqqqMHPmTK2bFXJ5SrRr+KJZBM31gkTq0k0QAsDLL7+MefPmwe12o6ioCHfddZfiv6Fk0SGaNXzRhhrXCxKpR9MgLCwsRGFhoe91QUEBtm/frtrvKb0tLlqBocaKMJG2hDp9JpbjrtQitSLM47aI1CNUEOrxMZZSwpnLZ4jUJVQQeufnnro3R7NhcSAp4azHniyRkeiqWBIPeis6SCme8LgtInUJF4RaC1YYiRTOXD5DpC4GoUKkVH5DVa2lfFZvPVkiI2EQKkDqspxQc33ez7539DzGDf8ubk1LYc+PKI6EKpaoRWoxI1hhxP+zbg/w58/+xuowUZwxCBUQLOCCrfsLVrUenZcOs+nm72R1mCh+ODRWQGAxA0DIoXLgXF9xfgZm3D8YGw7+Fe4uj+99VoeJ4odBqBD/gFu0u17Wg53Kxg1FQVZ/HD7dgr7WZFx1dnKOkCiOGIRQfq+v1HV/gb/L4CPShvBBqPRBDN5wm1aUG7Znp5cDIIiIQSj7+cTBeMOvrzUZb1Wd8/UEw4WbEr9LRMoQvmoc60EM/gcibDhwRvKeYD0eAEEkKuF7hLFuXwtcB2hOMsHd5YkYbtw2R6QfwgchENv2tcDCSKS5QaV+l4iUwyCMEXt2RImPQagA9uyIEpvwxRIiIvYI/fAhSkRiEjYIA0NPyQXODFSixCJkEAYLPbkLnEOFHXeMECUeIecIg4WenAXO4Z4qxwctESUeIYMwWOjJecJduLDjjhGixCPk0DjU2r9wy2D8h8LhTpfhukKixCNkEALy1v4Fm/cLF3ZcV0iUWIQNQjmCDYWXThjOsCMyCCHnCOWSW0gJfFYJEekbe4QSSJ3349IZosQkTBAebW7D1lP1URcwpMz78bBVosQkxNC4stGBFYcuhXxesFLDWS6dIUpMQvQID59ugcvd/ajMwJ6aksNZLp0hSkxC9AhH56XD8u1T1AN7akrvBCnOz2BFmSjBCNEjLM7PwIIxA3HOab2ppyb10ZtEZFxCBCEAjMpOxVSb7ab3OZwlImGCMBzuBCESG4NQZTybkEj/hCiWaCXccV1EpB8MwgCh1hRGs9aQZxMSJQYGoZ9QPbhoe3ZcYE2UGBiEfkL14KLt2ck57JWItMMg9OPfgzObgL7W5Jvel9uz4wJrIv1j1dhPcX4GphXlYsPBv8Ld5cFbVedQkNU/7FpDVoWJEh+DMMBVZyfcXTfvSw621pDHbhEZA4fGAeQMg1kVJjIG9ggDyNlyx33KRMbAIAxC6pY77lMmMgYGYYy4T5ko8XGOkIiExyAkIuFxaBwnXG9IpF+a9ggrKysxd+5c3+uPP/4YDzzwAEpLS1FaWopjx45p2Drl8BQaIn3TrEdYXl6Oqqoq2PxOjW5oaEBZWRnGjRunVbNUwcd8EumbZj3CESNGYMmSJT3ea2howM6dOzFlyhSsWLEC169f16ZxCuMpNET6ZvJ4PB41f2DHjh3YtGlTj/cqKipw5513ora2Fu+//z5Wr14NAHj77bfxwAMPIDMzE4sXL8aQIUPw5JNPhvzuuro6WCwWSe1wOp2wWq3R30iMjja34dOv2jFiUG+Myk5V/fe0vt944/0aWyz3awvyrKJAqg+NS0pKUFJSIunaf/3Xf0W/fv0AAD/96U+xd+/esNdbLBZJNwkAdrtd8rVqsNmAqXH8Pa3vN954v8YW7f3a7XZJ1+lm+YzH48H48ePx97//HQBQU1ODYcOGadyq4KI5rZqI9Es3y2dMJhPKy8sxc+ZMWK1W3H777fj5z3+u2u/5L2cBIHlpC0+cITIeTYOwsLAQhYWFvtdFRUUoKipS/Xf9w+z9YxcAAB3uLknBxgowkfHoZmgcT/5h1uHuQoe7C4C0o7RYASYyHiGD0D/MUsxJSDEn+f584cq1sHN/fA4JkfHoZo4wngKPzwKALbXnUX3mMvY3teDQqRbMuH8wCrL6h5xHZAASGYeQQQjcfHzW4dMt6HB3D4vdHmD9gTPolZSEDneX7HlEIkosQg6Ngxmdlw6z6cbrLg98c4dy5xGJKLEwCL9VnJ+BGfcPhjmpOw0D5w69f2aBhMh4hB0aB1M2bmjIeUH/P3NYTGQsDMIAgXOHof5MRMbBoTERCY9BSETCYxASkfAYhEQkPAYhEQmPQUhEwmMQEpHwGIREJDwGIREJj0FIRMJjEBKR8BiERCQ8BiERCY9BSETCEyYIjza38aHsRBSUEOcRVjY6sOLQJbjcHj5zhIhuIkQQHj7dApfbA6D7mSNbas/ztGki8hFiaDw6Lx0W841nkVSfuYx3as5j1tYTHCoTkRhBWJyfgQVjBuKpe3Nw3+Bb+EQ6IupBiKExAIzKTsVUmw2VjQ4cPXsF7Z1uPpGOiAAIFIRexfkZWDP5bs4REpGPcEEI3PykOiISmxBzhERE4TAIiUh4DEIiEh6DkIiExyAkIuExCIlIeAxCIhIeg5CIhMcgJCLhMQiJSHgMQiISHoOQiITHICQi4TEIiUh4DEIiEh6DkIiExyAkIuExCIlIeAxCIhIeg5CIhMcgJCLhMQiJSHiaPM7z6tWrKCsrQ2trKzo7O7FgwQLcfffdqKurw7Jly2A2m1FUVISZM2dq0TwiEowmPcK3334bo0aNwrvvvovly5dj6dKlAIDFixdj1apV2Lp1K06ePImGhgYtmofKRgcW7a5HZaNDk98novjSpEf49NNPIyUlBQDgdrthsVjQ2tqKjo4OZGdnAwCKiopQU1ODYcOGxbVtlY0OzNp6Au2dbuw4fhFrJt/Nh8ETGZzqQbhjxw5s2rSpx3sVFRW488470dLSgrKyMrz00ktobW1FWlqa75rU1FRcuHAh7He7XC7Y7XZJ7XA6nZKu3VP7Ndo73QCA9k439tSeQqbpiqTf0BOp92sUvF9jU/t+VQ/CkpISlJSU3PR+U1MT5syZgxdffBH33HMPWltb0dbW5vv7trY29OvXL+x3WywW2Gw2Se2w2+2Srh3vcWDf2e4eYe9kM8YXDoHNlng9Qqn3axS8X2OL9n6lhqcmQ+MzZ87g+eefx29/+1vccccdAIC0tDQkJyejubkZWVlZqKqq0qRYUpyfgTWT78bh0y0YnZfOYTGRADQJwlWrVqGjowPLli0D0B2C69evx8svv4x58+bB7XajqKgId911lxbNQ3F+BgOQSCCaBOH69euDvl9QUIDt27fHuTVEJDouqCYi4TEIiUh4DEIiEh6DkIiExyAkIuExCIlIeAxCIhIeg5CIhMcgJCLhMQiJSHgMQiISHoOQiITHICQi4TEIiUh4DEIiEh6DkIiExyAkIuExCIlIeCaPx+PRuhHRqqurg8Vi0boZRKRTLpcLBQUFEa9L6CAkIlICh8ZEJDwGIREJj0FIRMJjEBKR8BiERCQ8BiERCa+X1g2Il8rKSnz00UdYtWoVgO41iMuWLYPZbEZRURFmzpypcQuV5fF4MGbMGHz/+98HABQUFGDu3LnaNkoFXV1dWLJkCZqampCSkoLy8nLk5ORo3SxVPfroo+jbty8AIDMzE8uXL9e4Reo4efIkXn/9dWzevBnnz5/HggULYDKZkJeXh8WLFyMpSbl+nBBBWF5ejqqqKthsNt97ixcvxtq1a5GVlYXp06ejoaEBw4YN07CVympubsawYcOwYcMGrZuiqn379qGjowPbtm1DXV0dVqxYgfXr12vdLNW4XC4AwObNmzVuibo2btyIPXv2oHfv3gCA5cuXY/bs2SgsLMSiRYvwySefoLi4WLHfE2JoPGLECCxZssT3urW1FR0dHcjOzobJZEJRURFqamq0a6AKGhoa4HA4UFpaimeeeQZnz57Vukmq+Mtf/oLRo0cD6O711tfXa9widX3++edob2/HtGnT8NRTT6Gurk7rJqkiOzsba9eu9b1uaGjAPffcAwAYM2YMjhw5oujvGapHuGPHDmzatKnHexUVFXj44YdRW1vre6+1tRVpaWm+16mpqbhw4ULc2qm0YPe9aNEiTJ8+HQ899BCOHz+OsrIy7Ny5U6MWqifwn6XZbMb169fRq5eh/tX2sVqt+MUvfoGSkhJ88cUXeOaZZ/DRRx8Z7n7HjRuHixcv+l57PB6YTCYA3f+9Xr16VdHfM9T/eiUlJSgpKYl4XVpaGtra2nyv29ra0K9fPzWbpqpg993e3g6z2QwAGDlyJBwOR49/mYwi8J9lV1eX4ULBX25uLnJycmAymZCbm4v+/fujpaUF3/3ud7Vumqr85wPV+O9ViKFxoLS0NCQnJ6O5uRkejwdVVVUYOXKk1s1S1Lp163y9xM8//xyDBg0yXAgC3dMehw4dAtBdABsyZIjGLVLXBx98gBUrVgAAHA4HWltbkZ6ernGr1Jefn+8b1R06dEjx/16N+3+dEbz88suYN28e3G43ioqKcNddd2ndJEVNnz4dZWVlOHjwIMxms2Eri8XFxaiursakSZPg8XhQUVGhdZNUNXHiRPz7v/87Jk+eDJPJhIqKCkP3gL3mz5+P3/zmN3jjjTdw2223Ydy4cYp+P0+fISLhCTk0JiLyxyAkIuExCIlIeAxCIhIeg5CIhMcgJCLhMQiJSHgMQkpYpaWlqK6uBgCsXr0a5eXlGreIEpXxl6STYc2aNQtr1qzB5cuXYbfbDX38FqmLO0sooT355JO4du0a3nnnHaSlpeHChQtYv349WltbsWbNGq2bRwmCQ2NKWE1NTWhpaUFKSorvKK6srCzD7zcm5TEIKSFdunQJ8+bNw5tvvonevXvj8OHDWjeJEhiDkBJOe3s7fv3rX2PBggW4/fbb8atf/Qrr1q3TulmUwDhHSIbyj3/8A6tXr8aRI0dQUlKCX/7yl1o3iRIAg5CIhMehMREJj0FIRMJjEBKR8BiERCQ8BiERCY9BSETCYxASkfAYhEQkvP8PWcmQU48IW68AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_signals = 250\n",
    "x1 = np.linspace(-10, 10, n_signals) + .1 * randn(n_signals)\n",
    "x2 = 1.5 * x1 + 2 * randn(n_signals)\n",
    "data = pd.DataFrame({'$x_1$': x1, '$x_2$': x2})\n",
    "ax = data.plot.scatter(x=0, y=1, s=10, title='2D Noisy Data', figsize=(7,8))\n",
    "ax.set_aspect('equal')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compute Principal Components "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.470611Z",
     "start_time": "2018-12-27T18:10:20.459629Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.54381787, -0.83920327],\n",
       "       [ 0.83920327, -0.54381787]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "pca.fit(data)\n",
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.476159Z",
     "start_time": "2018-12-27T18:10:20.471829Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.00024229,  0.03183435])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = pca.mean_\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.484512Z",
     "start_time": "2018-12-27T18:10:20.477581Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.54381787],\n",
       "       [-0.83920327]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc1, pc2 = np.split(pca.components_.T, 2, axis=1)\n",
    "pc1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Check share of explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.493176Z",
     "start_time": "2018-12-27T18:10:20.485793Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.98929523, 0.01070477])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Components are orthogonal to each other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.500983Z",
     "start_time": "2018-12-27T18:10:20.494172Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(pc1.T, pc2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot Principal Components as new Basis Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figure shows how the first and second principal components align with the directions of maximum variance while being orthogonal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.508197Z",
     "start_time": "2018-12-27T18:10:20.502316Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "l1, l2 = pca.singular_values_ / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:20.663371Z",
     "start_time": "2018-12-27T18:10:20.509218Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = data.plot.scatter(x=0, y=1, s=15, title='Principal Component Vectors', figsize=(6,8))\n",
    "ax.set_aspect('equal')\n",
    "origin_x, origin_y = pca.mean_\n",
    "dx1, dy1 = np.squeeze(pc1.T) * l1\n",
    "dx2, dy2 = np.squeeze(pc2.T) * l2\n",
    "pc1_arrow = ax.arrow(origin_x, origin_y, dx1, dy1,  width=.2, color='k')\n",
    "pc2_arrow = ax.arrow(origin_x, origin_y, dx2, dy2,  width=.2, color='r')\n",
    "plt.legend([pc1_arrow, pc2_arrow], \n",
    "           ['Principal Component 1', 'Principal Component 2'], \n",
    "           fontsize='small')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Project 2D data onto the first Principal Component"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following figure demonstrates how the first principal component minimizes the reconstruction error, measured as the sum of the distances between the data points and the new axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:21.016248Z",
     "start_time": "2018-12-27T18:10:20.664483Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# de-mean data, convert to numpy array\n",
    "data_ = data.sub(data.mean())\n",
    "X_ = data_.values\n",
    "x_, y_ = X_.T\n",
    "ax = pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$', \n",
    "                                                           y='$x_2$', \n",
    "                                                           s=15, \n",
    "                                                           title='1D Projection', \n",
    "                                                           figsize=(6, 12))\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# plot first component\n",
    "t = np.linspace(-25, 25, n_signals)\n",
    "pc_x, pc_y = t * pc1\n",
    "ax.plot(pc_x, pc_y, c='k', lw=1)\n",
    "\n",
    "# project original data on first component\n",
    "proj_x, proj_y = (X_.dot(pc1) * pc1.T).T\n",
    "ax.scatter(proj_x, proj_y, s=15, c='k')\n",
    "\n",
    "# plot link from data to projected points\n",
    "lines_x, lines_y = np.c_[x_, proj_x], np.c_[y_, proj_y]\n",
    "ax.plot(lines_x.T, lines_y.T, lw=1, c='darkgrey')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot 1D Representation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:21.085255Z",
     "start_time": "2018-12-27T18:10:21.017173Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ECgBgEoECAJhEoAAAJhEoAIBJBAoAYBKBAgCYRKAAACYRKACASQQKAGASgQIAmESgAAAmESgAgEkECgBgEoECAJhEoAAAJhEoAIBJBAoAYBKBAgCYRKAAACYRKACASQQKAGASgQIAmESgAAAmESgAgEkECgBgEoECAJhEoAAAJhEoAIBJBAoAYBKBAgCYRKAAACYRKACASQQKAGASgQIAmESgAAAmESgAgEkECgBgEoECAJhEoAAAJhEoAIBJBAoAYBKBAgCYRKAAACYRKACASS7HcZxkBx88eFBpaWkdOR8AQA9XV1ensWPHtjquTYECAKCz8CM+AIBJBAoAYBKBAgCYRKAAACYRKACASQQKAGBSpwWqurpa8+bN08MPP6wZM2bowIEDkhr/bVV+fr5mzpypl156qbOm02Pt3LlTv/71ryPvs77tIxQKadmyZZoxY4YeeeQRlZWVdfWUeowPP/xQjzzyiCSprKxMs2bN0uzZs/Xb3/5WoVCoi2fXfdXX12vRokWaPXu2pk+frnfffbf7ra/TSdasWeO8/vrrjuM4zunTp528vDzHcRznoYcecsrKypxQKOT84he/cI4cOdJZU+pxnn32WWfy5MnOk08+GfkY69s+duzY4SxevNhxHMc5cOCAM2/evC6eUc/w6quvOg8++KCTn5/vOI7jzJ0713n//fcdx3GcpUuXOn/961+7cnrd2p///GdnxYoVjuM4zqVLl5xJkyZ1u/XttO+gfv7zn2vmzJmSpGAwqLS0NPn9fgUCAQ0ePFgul0sTJkzQP//5z86aUo+Tm5urZ555JvI+69t+9u3bp4kTJ0qSxo4dqyNHjnTxjHqGwYMHa+3atZH3jx49qnHjxkmS7r33XpWUlHTV1Lq9H/3oR1qwYEHkfY/H0+3Wt0MCtWnTJj344IMx/505c0bp6emqqKjQokWLtHDhQvn9fvl8vsjn9e7dW9XV1R0xpR4l0foeOnRIU6ZMkcvlioxjfdtP/Fp6PB41NDR04Yx6hsmTJ8vr9UbedxwnsofZrzemd+/e8vl88vv9Kigo0JNPPtnt1tfb+pC2y8/PV35+fpOPHz9+XAsXLtTTTz+tcePGye/369q1a5Hbr127pszMzI6YUo/S3PrG8/l8rG87iV/LUCgU88SK9uF2X/+amf16486fP6/58+dr9uzZmjp1qgoLCyO3dYf17bQf8Z06dUoLFizQypUrNWnSJEmND/qUlBSdPXtWjuPo73//u773ve911pR6PNa3/eTm5qq4uFhS4y+eZGdnd/GMeqacnBzt3btXklRcXMx+vQGVlZV67LHHtGjRIk2fPl1S91vfTvsScOXKlQoEAvrd734nqfHJc/369Vq+fLmeeuopBYNBTZgwQWPGjOmsKX0jsL7t4/7779c//vEPzZw5U47j6LnnnuvqKfVIixcv1tKlS7Vq1SoNGzZMkydP7uopdVsvv/yyrl69qnXr1mndunWSpN/85jdasWJFt1lf/po5AMAk/qEuAMAkAgUAMIlAAQBMIlAAAJMIFADAJAIFADCJQAEATOJvtQA36Gc/+5mqqqokSR9//LH+8Ic/6IEHHujiWQHdH/9QF2gnRUVF2rt3r1atWiWPx9PV0wG6Pb6DAtrB5s2bVVxcrLVr1+rzzz/X+vXr5ff79eKLL3b11IBui9eggBu0fft2bdmyRWvWrFFKSoqysrL4W31AO+A7KOAGvPfeeyoqKtIrr7yitLS0rp4O0KPwHRRwA5YsWaLy8nLNmjVLP/nJT7Rp06aunhLQY/BLEkA7u3z5sl544QWVlJQoPz9fc+fO7eopAd0SgQIAmMSP+AAAJhEoAIBJBAoAYBKBAgCYRKAAACYRKACASQQKAGASgQIAmPT/inL93mnbzPgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "projection1D = data_.dot(pc1)\n",
    "ax = projection1D.rename(columns={0: '$z_1$'})\\\n",
    "    .assign(x2=0).plot.scatter(x='$z_1$', y='x2', s=10, title='1D Signal')\n",
    "ax.get_yaxis().set_visible(False)\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Compare to Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the below figure contrasts PCA with supervised OLS, which approximates the outcome variable (here we choose x2) by a (one-dimensional) hyperplane computed from the (single) feature. \n",
    "\n",
    "The vertical lines highlight how OLS minimizes the distance along the outcome axis, in contrast with PCA that minimizes the distances orthogonal to the hyperplane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:21.421309Z",
     "start_time": "2018-12-27T18:10:21.086167Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stefan/.pyenv/versions/miniconda3-latest/envs/ml4t/lib/python3.7/site-packages/ipykernel_launcher.py:10: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x864 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$', \n",
    "                                                           y='$x_2$', \n",
    "                                                           s=15, \n",
    "                                                           title='PCA vs OLS', \n",
    "                                                           figsize=(6, 12))\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "# get OLS line\n",
    "reg_X = np.column_stack((x_, np.ones_like(x_)))\n",
    "(m, b), _, _, _ = lstsq(reg_X, y_)\n",
    "reg_y = m * x_ + b\n",
    "ax.plot(x_, reg_y, c='k')\n",
    "\n",
    "# plot residuals\n",
    "lines_x, lines_y = np.c_[x_, x_], np.c_[y_, reg_y]\n",
    "ax.plot(lines_x.T, lines_y.T, lw=1)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Combined Figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below figure is included in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:50.205991Z",
     "start_time": "2018-12-27T18:10:49.434168Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/stefan/.pyenv/versions/miniconda3-latest/envs/ml4t/lib/python3.7/site-packages/ipykernel_launcher.py:49: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=3, figsize=(14, 6), sharex=True, sharey=True)\n",
    "\n",
    "title='Principal Component Vectors'\n",
    "data.plot.scatter(x=0, y=1, s=15, ax=axes[0], title=title)\n",
    "axes[0].set_aspect('equal')\n",
    "\n",
    "origin_x, origin_y = pca.mean_\n",
    "dx1, dy1 = np.squeeze(pc1.T) * l1\n",
    "dx2, dy2 = np.squeeze(pc2.T) * l2\n",
    "pc1_arrow = axes[0].arrow(origin_x, origin_y, dx1, dy1,  width=.2, color='k')\n",
    "pc2_arrow = axes[0].arrow(origin_x, origin_y, dx2, dy2,  width=.2, color='r')\n",
    "axes[0].legend([pc1_arrow, pc2_arrow],\n",
    "               ['Principal Component 1', 'Principal Component 2'],\n",
    "               fontsize='small')\n",
    "\n",
    "# de-mean data, convert to numpy array\n",
    "data_ = data.sub(data.mean())\n",
    "X_ = data_.values\n",
    "x_, y_ = X_.T\n",
    "pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$',\n",
    "                                                      y='$x_2$',\n",
    "                                                      s=15,\n",
    "                                                      title='1D Projection',\n",
    "                                                      ax=axes[1])\n",
    "axes[1].set_aspect('equal')\n",
    "\n",
    "# plot first component\n",
    "t = np.linspace(-20, 20, n_signals)\n",
    "pc_x, pc_y = t * pc1\n",
    "axes[1].plot(pc_x, pc_y, c='k', lw=1)\n",
    "\n",
    "# project original data on first component\n",
    "proj_x, proj_y = (X_.dot(pc1) * pc1.T).T\n",
    "axes[1].scatter(proj_x, proj_y, s=15, c='k')\n",
    "\n",
    "# plot link from data to projected points\n",
    "lines_x, lines_y = np.c_[x_, proj_x], np.c_[y_, proj_y]\n",
    "axes[1].plot(lines_x.T, lines_y.T, lw=1, c='darkgrey')\n",
    "\n",
    "pd.DataFrame({'$x_1$': x_, '$x_2$': y_}).plot.scatter(x='$x_1$',\n",
    "                                                      y='$x_2$',\n",
    "                                                      s=15,\n",
    "                                                      title='PCA vs OLS',\n",
    "                                                      ax=axes[2])\n",
    "ax = axes[2].set_aspect('equal')\n",
    "\n",
    "# get OLS line\n",
    "reg_X = np.column_stack((x_, np.ones_like(x_)))\n",
    "(m, b), _, _, _ = lstsq(reg_X, y_)\n",
    "reg_y = m * x_ + b\n",
    "ax = axes[2].plot(x_, reg_y, c='k')\n",
    "\n",
    "# plot residuals\n",
    "lines_x, lines_y = np.c_[x_, x_], np.c_[y_, reg_y]\n",
    "ax = axes[2].plot(lines_x.T, lines_y.T, lw=1, c='darkgrey')\n",
    "\n",
    "fig.tight_layout()\n",
    "# fig.savefig('figures/pc_comparison', dpi=600);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Recover Data using Inverse Transformation 1D => 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:10:53.455912Z",
     "start_time": "2018-12-27T18:10:53.320798Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "recovered_data = projection1D.dot(pc1.T).rename(columns={0: '$x_1$', 1: '$x_2$'})\n",
    "\n",
    "rms_reconstruction_error = np.sqrt(np.mean(np.sum(np.square(recovered_data-data_), axis=1)))\n",
    "\n",
    "rss_data = np.sqrt(np.sum(data_.values**2))\n",
    "\n",
    "relative_loss = rms_reconstruction_error / rss_data\n",
    "\n",
    "title='Reconstructed Data | Error: {:.2%}'.format(relative_loss)\n",
    "ax = recovered_data.plot.scatter(x=0, y=1, title=title, c='k')\n",
    "ax.set_aspect('equal')\n",
    "data_.plot.scatter(x=0, y=1, s=10, ax=ax, figsize=(4,8))\n",
    "plt.legend(handles=[Patch(color='k', label='Recovered'),  \n",
    "                    Patch(label='Original Data')])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Projection and inverse transformation lead to the same result"
   ]
  },
  {
   "cell_type": "code",
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     "start_time": "2018-12-27T18:10:56.203254Z"
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      "text/plain": [
       "True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(recovered_data, X_.dot(pc1) * pc1.T)"
   ]
  }
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